Algorithms for Geometric Problems of Practical Interest

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Computational geometry as a field deals with the algorithmic aspects of geometric problems. Most of the existing research has been restricted, however, to problems involving straight lines in two dimensions. The goal of this project is to develop improved computational methods for both curved objects and three-dimensional objects and then to develop efficient algorithms for a collection of optimization problems, including inner and outer approximation of curved and three-dimensional objects, three-dimensional mesh generation, and pre-fabrication partitioning of both rectilinear and fixed-orientation of VLSI designs.